RNA Folding and Matrix Field Theory

Henri Orland, CEA Saclay

After reviewing some elementary properties of RNA, we show how the RNA folding problem can be exactly formulated as an NxN matrix field theory. This formulation induces a natural classification of RNA structures by their topological genus. We show that secondary structures without pseudo-knots are the planar structures with zero genus, whereas pseudo-knots correspond to RNA structures with higher genii. This classification allows for the exact enumeration of RNA structures. We also show how these concepts can be used to make accurate predictions of real biological RNA molecules.